(HP71B) Eigenvalues of Symmetric Real Matrix

[Werner]

No, it isn’t Jacobi.
It looks a bit like it, but it transforms the whole matrix in one go, slowly (but ever faster, and ultimately quadratically) converging to a diagonal matrix.
I understand the Cayley transform Q=(I-B)*inv(I+B), but not why and how the skew-symmetric matrix B would make Q an estimate for the eigenvectors (and not eigen*values* as written on pg 149 of the AFH, a typo), and why it would converge at all.
Jacobi itself is simple, just setting a single off-diagonal element to zero. The resulting formula is similar, but not the same -

Cheers, Werner